Problem: Simplify the following expression: $y = \dfrac{5a^2 - 20a - 225}{a + 5} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ y =\dfrac{5(a^2 - 4a - 45)}{a + 5} $ Then we factor the remaining polynomial: $a^2 {-4}a {-45} $ ${5} {-9} = {-4}$ ${5} \times {-9} = {-45}$ $ (a + {5}) (a {-9}) $ This gives us a factored expression: $\dfrac{5(a + {5}) (a {-9})}{a + 5}$ We can divide the numerator and denominator by $(a - 5)$ on condition that $a \neq -5$ Therefore $y = 5(a - 9); a \neq -5$